Abstract
We present a three-parameter family of solutions to the stationary axisymmetric Einstein equations that describe differentially rotating disks of dust. They have been constructed by generalizing the Neugebauer—Meinel solution of the problem of a rigidly rotating disk of dust. The solutions correspond to disks with angular velocities depending monotonically on the radial coordinate; both decreasing and increasing behaviour is exhibited. In general, the solutions are related mathematically to Jacobi's inversion problem and can be expressed in terms of Riemann theta functions. A particularly interesting two-parameter subfamily represents Bäcklund transformations to appropriate seed solutions of the Weyl class.
Similar content being viewed by others
REFERENCES
Kerr, R. (1963). Phys. Rev. Lett. 11, 237.
Neugebauer, G., and Meinel, R. (1993). Astrophys. J. 414, L97.
Neugebauer, G., and Meinel, R. (1995). Phys. Rev. Lett. 75, 3046.
Neugebauer, G., Kleinwächter, A., and Meinel, R. (1996). Helv. Phys. Acta 69, 472.
Ernst, F. J. (1968). Phys. Rev. 167, 1175.
Kramer, D., and Neugebauer, G. (1968). Commun. Math. Phys. 7, 173.
Maison, D. (1978). Phys. Rev. Lett. 41, 521.
Belinski, V. A., and Zakharov, V. E. (1978). Zh. Eksper. Teoret. Fiz. 75, 195.
Harrison, B. K. (1978). Phys. Rev. Lett. 41, 119.
Neugebauer, G. (1979). J. Phys. A 12, L67.
Neugebauer, G. (1980). J. Phys. A 13, L19.
Neugebauer, G. (1980). J. Phys. A 13, 1737.
Korotkin, D. A. (1989). Theor. Math. Phys. 77, 1018.
Korotkin, D. A. (1993). Class. Quantum Grav. 10, 2587.
Meinel, R., and Neugebauer, G. (1996). Phys. Lett. A 210, 160.
Korotkin, D. A. (1997). Phys. Lett. A 229, 195.
Meinel, R., and Neugebauer, G. (1997). Phys. Lett. A 229, 200.
Kleinwächter, A. (1995). ”Untersuchungen zu rotierenden Scheiben in der Allgemeinen Relativitätstheorie.” Ph.D. Dissertation, Friedrich-Schiller-Universität Jena.
Bardeen, J. M., and Wagoner, R. V. (1971). Astrophys. J. 167, 359.
Meinel, R. (1998). In Recent Developments in Gravitation and Mathematical Physics, A. García, C. Lämmerzahl, A. Macías, T. Matos, and D. Nuñez, eds. (Science Network Publishing, Konstanz); gr-qc/9703077.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Ansorg, M., Meinel, R. Differentially Rotating Disks of Dust. General Relativity and Gravitation 32, 1365–1380 (2000). https://doi.org/10.1023/A:1001950922865
Issue Date:
DOI: https://doi.org/10.1023/A:1001950922865